Half a dozen F-18 fast jets streak across the sky, while below, others are flung off the top of the sprawling flight deck by steam catapult.

And In the midst of this display of naval power sits Rear Admiral Nora Tyson, the first woman to command a US carrier strike group. Adm Tyson is in charge of 75 jets, helicopters and other aircraft – together worth $45bn – plus a cluster of cruisers and destroyers, and nearly 10,000 men and women.

Earlier this month the 53-year-old was overseeing their part along with ships from the Royal Navy, France and Spain, in an international exercise off the coast of Britain sailing off to eventually support operations in Afghanistan.

Tyson commands the strike group from the USS George H W Bush, America's newest supercarrier and one of the world's biggest warships.

"What's there not to like?" she says, as an F-18 does a low-level flypast overhead." I feel very fortunate to be in this job – and very humbled."

Tyson joined the US navy in 1979 and whenUS law changed in 1993, allowing women to go on naval combat missions, she was made navigator of the carrier USS Enterprise before commanding an assault ship.

Later this year, she will be promoted to a two-star admiral and has become an inspiration for the other 44,000 women in the country's 325,000-strong navy.

"I hope I'm the first of many," she says.

But the rise of women through the ranks has not been without controversy. There have been numerous cases in the US in the past 20 years of sexual assaults on women while they've been serving overseas. And, of course, there are plenty of instances of sexual discrimination. Adm Tyson declines to answer questions on these subjects, referring me to the Washington press desk.

"I would love Britain to have one," she says, and suddenly beams.

"I think if women are mentally and physically capable of doing a job there's no reason not to be able to," she says.